Understanding Philosophy via Reconstruction

Disclaimer: I'm a total piker when it comes to philosophy. I'm a mathematician.

But I read technical physics papers thinking "What problem are they trying to solve? What's the essence of the problem? How can I formulate this as an exercise? How can I reconstruct their solution? What's the simplest explanation of their solution?"

I end up abstracting away, formalizing, and presenting the problem(s) and possible solution(s). This is how I operate, and I see no reason why I cannot do it here.

In the long term, I'd like to formalize Hegel's philosophy. But that requires formalizing Kant, Hume, Spinoza, Descartes, Aristotle, and probably quite a few others I'm forgetting.

My naive approach treats each philosopher as his/her own "paradigm", with their own "language" and methodology. More precisely, each text describes a formal system, usually acting as a "component" or "subsystem" for the philosopher in question. And this overarching system for a given may change over time (see, e.g., Wittgenstein).

Initially I'll start with Aristotle, because his logic is not what "modern logic" appears to be. Plus his writing appears to be critical in understanding Kant, Hegel, and many others.

Problems with Formalization

As I read Grice's Studies in the Way of Words, specifically chapters 2 and 3, there is no "mechanical" way to translate philosophy texts into formal logic. It's an art, not a science.

Following Sebastian Lutz's Artificial Language Philosophy of Science is a source of inspiration for the idea of generating a language for the problem...which fits into the "Lisp programming language perspective" that one should grow a language.

When it comes to defining terms, this too is an art (c.f., Hansson's How to define: a tutorial). I may be forced to leave a term undefined (e.g., "A term philosopher Joe leaves undefined/vague").

The underlying aim is clarifying what the concepts are. Formalization serves as little more than a familiar framework to me, and pretending that a philosopher is a domain specific language fits my world-view.

For more diverse perspectives on formalization, see also Michael Baumgartner's Informal Reasoning and Logical Formalization, and Michael Baumgartner and Timm Lampert's Adequate Formalization. Baumgartner seems to argue that there are degrees of formalization, and we only need an adequate formalization...not a complete formalization. We should not first consider whether the projected formalized argument is valid before even attempting formalizing it.

We should probably note the "controversy" of formalization has been discussed since the '70s, if not earlier. It will probably continue being discussed until time ends.